音速於空氣中的速率問題(20分)HELP 我諗到好頭痛!

In fact, there is another formula relating sound wave velocity with density,
given by:
v = (B/d)^(1/2),
where v is the velocity of sound wave, B is the bulk constant and d is density.
From the equation, we see that actually velocity of sound wave is inversely proportional to density, which means it is directly proportional to temperature.
Intuitively, when density increases, there is lower concentration of particles to transmit the energy of sound wave. As sound wave is a mechanical wave, lower concentration means lower velocity of the wave. And when temperature decreases, the density decreases. Hence decreased temperature leads to lower velocity of sound wave.
Note that despite the fact wave velocity is inversely propotional to density of medium, sound wave travels fastest in solid, faster in liquid and slowest in air. This is because in solid, although desity increases, the bulk constant increases at a larger extent than that of ddensity, so sound wave travels faster.

Air molecules move randomly. This radom speed dpepends on temperature. The higher the temperature, the higher is the random speed. That is, air molecules move more vigorously at high temperature.

Sound wave travels in air by the transmission of vibrations of air molecules. This vibrational transmission could only take place when there are collisions between air molecules. When air molecules collide in their random motion (such motion is sometimes called thermal motion), this helps to transmit vibrations and hence sound wave.

Thus, it is not difficult to see that the higher the temperature, the more random collisions occur between air molecules because of their higher speed, leading to a faster transmission of sound wave vibrations.